Exercise 1.2, Unit-1, SETS, Mathematics 7, Punjab Curriculum and Textbook Board

EXERCISE 1.2 

1. Find the union of the following sets. 

(i) A = {1,3,5}, B = {1,2,3,4} 

Solution: 

A = {1,3,5}, B = {1,2,3,4} 

A U B  = {1,3,5} U {1,2,3,4}

           = {1,2,3,4,5} ......Ans

(ii) S = {a, b, c}, T = {c, d, e} 

Solution: 

S = {a, b, c}, T = {c, d, e} 

S U T = {a, b, c} U {c, d, e}

           = {a, b, c, d, e} ......Ans

(iii) X = {2,4,6,8,10}, Y = {1,5,10} 

Solution:  

X = {2,4,6,8,10}, Y = {1,5,10} 

X U Y = {2,4,6,8,10} U {1,5,10}

           = {1,2,4,5,6,8,10} ......Ans

(iv) C = {i, o, u}, D = {a, e, o}, E = {i, e, u} 

Solution:  

C = {i, o, u}, D = {a, e, o}, E = {i, e, u} 

(C U D) U E = ({i, o, u} U {a, e, o}) U {i, e, u} 

                      = {a, e, i, o, u} U {i, e, u} 

                      = {a, e, i, o, u} ......Ans

(v) L = {3, 6, 9, 12}, M = {6, 12, 18, 24}, N = { 4, 8, 12, 16} 

Solution:  

L = {3, 6, 9, 12}, M = {6, 12, 18, 24}, N = { 4, 8, 12, 16} 

(L U M) U N = ({3, 6, 9, 12} U {6, 12, 18, 24}) U {4, 8, 12, 16} 

                      = {3, 6, 9, 12, 18, 24} U {4, 8, 12, 16} 

                      = {3, 4, 6, 8, 9, 12, 16, 18, 24} ......Ans

2. Find the intersection of the following sets. 

(i) P = {0, 1, 2, 3}, Q = {-3, -2, -1, 0}

Solution:  

P = {0, 1, 2, 3}, Q = {-3, -2, -1, 0} 

P ⋂ Q = {0, 1, 2, 3} ⋂ {-3, -2, -1, 0}

           = {0} ......Ans

(ii) M = {1, 2, ... , 10}, N = {1, 3, 5, 7, 9}

Solution: 

M = {1, 2, ... , 10}, N = {1, 3, 5, 7, 9} 

M ⋂ N = {1, 2, ... , 10} ⋂ {1, 3, 5, 7, 9}

           = {1, 3, 5, 7, 9} ......Ans

(iii) A = {3, 6, 9, 12, 15}, B = {5, 10, 15, 20}

Solution: 

A = {3, 6, 9, 12, 15}, B = {5, 10, 15, 20} 

A ⋂ B = {3, 6, 9, 12, 15} ⋂ {5, 10, 15, 20}

           = {15} ......Ans

(iv) U = {-1, -2 , -3}, V = {1, 2, 3}, W = {0, ±1, ±2}

Solution: 

U = {-1, -2 , -3}, V = {1, 2, 3}, W = {0, ±1, ±2}

(U ⋂ V) ⋂ W = ({ -1, -2 , -3} ⋂ {1, 2, 3}) ⋂ {0, ±1, ±2} 

                     = {   } ⋂ { 0, ±1, ±2 } 

                     = {   } ......Ans

(v) X = {a, l, m}, Y = {i, s, l, a, m}, Z = {l, i, o, n} 

Solution: 

X = {a, l, m}, Y = {i, s, l, a, m}, Z = {l, i, o, n} 

(X ⋂ Y) ⋂ Z = ({a, l, m} ⋂ {i, s, l, a, m}) ⋂ {l, i, o, n} 

                    = { a, l, m } ⋂ {l, i, o, n}  

                    = { l } ......Ans

3. If N = set of Natural numbers and W = set of Whole numbers,

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